UNIVERSITY OF TRINIDAD AND TOBAGO B.A.Sc. Utilities Engineering February 02, 2009
CCTD101B Engineering Thermodynamics (Lecture Notes 4) The First Law of Thermodynamics 4.
First Law of Thermodynamics.............................................................................................................1 4.1 Energy Balance for Closed Systems.............................................................................................1 4.2 Nature of Stored Energy................................................................................................................1 4.3 First Law Applied to Cyclic Processes.........................................................................................4 4.4 Power Cycles.................................................................................................................................4 4.5 Refrigeration and Heat Pump Cycle.............................................................................................5 4.5.1 Refrigeration Cycles..............................................................................................................5 4.5.2 Heat Pump Cycles..................................................................................................................6 4.6 The First Law Applied to Open Systems......................................................................................6
4.
First Law of Thermodynamics
4.1 Energy Balance for Closed Systems The only ways the energy of a closed system can be changed are through transfer of energy by work or by heat. Further, based on the experiments by Joule and others, a fundamental aspect of the energy concept is that energy is conserved; we call this the first law of thermodynamics. These considerations are summarized in words as follows:
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net amount of energy net amount of energy change∈the amount transferred ∈across transferred out across of energy contained = the systembounda ry by − the system boundary by ¿ the system during heat transfer during the work during the some time interval timeinterval time interval
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This word statement is just an accounting balance for energy and represents the Principle of Conservation of Energy. The energy balance can be expressed in symbols as: E2−E 1=Q−W 4.2 Nature of Stored Energy Energy can be stored in many forms such as potential, kinetic, electrical, magnetic, surface and other energies: Potential energy is the energy stored in a system as a result of its location in a gravitational field, and its magnitude is given by PE = mgz
CCTD101B –The First Law of Thermodynamics
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Kinetic energy is the energy stored in a system by virtue of the motion of the system, and its magnitude mV 2 KE 2 . is given by: Internal energy U is the form of energy stored in a system that is independent of gravity, motion, electricity, magnetism and surface tension. The internal energy is related to the PE and KE of the molecules of the substance and to the internal structure of the molecules. In the absence of motion, gravity, electricity, magnetism and surface tension, U = E. If motion and gravity are considered; mV 2 E U mgz 2 Introducing these types of energy, the energy balance can be alternatively written as: ∆ KE+∆ PE+ ∆U =Q−W For closed systems, the effects of gravity and motion are negligible. Ignoring the effects of electric, magnetic, solid distortion and surface tension, the first law applied to a closed system becomes: ∆ U =Q−W In analyzing systems, it is important to recognize that the location of system boundary can be relevant in determining whether a particular energy transfer is regarded as heat or work. For example, consider the figure below, in which three alternative systems are shown that include a quantity of gas (or liquid) in a rigid, well insulated container. In figure (a) the gas itself is the system. As current flows through the copper plate, there is an energy transfer from the copper plate to the gas. Since this energy transfer occurs as a result of the temperature difference between the plate and the gas, it is classified as a heat transfer. Next refer to figure (b) where the boundary is drawn to include the copper plate. It follows from the thermodynamic definition of work that the energy transfer that occurs as current crosses the boundary of this system must be regarded as work. Finally, in figure (c) the boundary is located so that no energy is transferred across it by heat or work.
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Example 4 kg of a certain gas is contained within a piston-cylinder assembly. The gas undergoes a process for which the pressure volume relationship is
pV 1.5=constant The initial pressure is 3 bar, the initial volume is 0.1 m 3, and the final volume is 0.2 m 3. The change in specific internal energy in the process is u2−u1 =−4.6 kJ /kg . There are no significant changes in kinetic and potential energy. Determine the net heat transfer for the process in kJ.
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4.3 First Law Applied to Cyclic Processes The energy balance for any system undergoing a thermodynamic cycle takes the form ∆ E cycle=Qcycle−W cycle where Qcycle and Wcycle represent net amounts of energy transfer by heat and work for the cycle. Since the system is returned to its original state after the cycle, there is no net change in energy. Therefore the equation reduce to Qcycle=W cycle This equation is an expression of the conservation of energy principle that must be satisfied by every thermodynamic cycle regardless of the sequence of processes followed by the system undergoing the cycle or the nature of the substances making up the system. The diagram below provides simplified schematics of two general classes of cycles; power cycles and refrigeration and heat pump cycles. In each case a system undergoes a cycle while communicating thermally with two bodies, one hot and the other cold. These bodies are systems located in the surroundings of the system undergoing the cycle. During each cycle there is also a net amount of energy exchanged with the surroundings by work.
4.4 Power Cycles Systems undergoing cycles of the type shown in figure (a) above deliver a net work transfer of energy to the surroundings during each cycle. Any such cycle is called a power cycle. From the first law equation for a cycle: W cycle =Q¿−Q out Where Qin represents the heat transfer of energy into the system from the hot body and Qout represents heat transfer out of the system to the cold body. From this equation, it is clear that Qin must be greater than Qout for a power cycle. The energy supplied by energy transfer to a system undergoing a power cycle is normally derived from fuel combustion. The energy Qout is normally discharged to the surrounding atmosphere or a nearby body of water.
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The performance of a system undergoing a power cycle can be described in terms of the extent to which the energy added by heat Qin is converted to a net work output, Wcycle. The extent of the energy conversion form heat to work is called the thermal efficiency, η W η= cycle Q¿ Introducing the power cycle equation: Q¿ −Qout Q η= =1− ¿ Q¿ Qout Since energy is conserved, it follows that thermal efficiency can never be greater than unity (100%). Experience with actual power cycles show that the value of the thermal efficiency is invariable less than unity due to heat rejection to the cold body. All the heat supplied cannot be converted into work. 4.5 Refrigeration and Heat Pump Cycle A refrigeration and heat pump cycle is shown in figure (b) above. For cycles of this type, Qin is the energy transferred by heat into the system undergoing the cycle from the cold body, and Qout, is the energy discharged by heat transfer from the system to the hot body. To accomplish these energy transfers requires a net work input Wcycle. The quantities Qin, Qout, and Wcycle are related by the energy balance and which for refrigeration and heat pump cycles take the form W cycle =Qout −Q¿ Since Wcycle is positive in this equation, it follows that Qout is greater than Q¿ . Refrigeration and heat pump cycles have different objectives. The objective of a refrigeration cycle is to cool a refrigerated space or maintain the temperature within a dwelling below that of the surroundings. The objective of a heat pump is to maintain the temperature within a dwelling or other building above that of the surroundings or provide heating for certain industrial processes that occur at elevated temperatures. Since refrigeration and heat pump cycles have different objectives, their performance parameters called coefficient of performances are defined differently. 4.5.1
Refrigeration Cycles
The performance of a refrigeration cycle can be described as the ratio of the amount of energy received by the system undergoing the cycle from the cold body, Q¿ to the net work into the system to accomplish this effect Wcycle. Thus the coefficient of performance, β, is Q β= ¿ W cycle Introducing the energy balance equation above, an alternative expression for β is Q¿ β= Qout −Q¿
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4.5.2
Heat Pump Cycles
The performance of heat pumps can be described as the ratio of the amount of energy discharged from the system undergoing the cycle to the hot body, Qout to the net work into the system to accomplish this effect Wcycle. Thus the coefficient of performance, γ is Q γ = out W cycle Introducing the energy balance equation above, an alternative expression for γ is Qout γ= Qout −Q¿ 4.6 The First Law Applied to Open Systems For open systems, the general statement of the first law is (Net Increase in stored energy of system) = (net amount of energy added to system as heat and all forms of work) + (stored energy of matter entering system) – (stored energy of matter leaving system)
Whenever matter crosses the boundary of a system, work is done on or by the system. Therefore, the total work for an open system is usually separated into two parts: (1) the work required to push a fluid in or out of the system, called flow work, and (2) all other forms of work. At any section where matter crosses a system boundary the flow work per unit mass is flow work per unit mass = pv Flow work does not apply a force to a moving system boundary or a torque to a rotating shaft, so it is treated separately from all other kinds of work. Therefore the symbol W means all work other than flow work, and the energy balance for an open system can be formulated as dE Q W m (e pv) m (e pv ) dt inlets outlets
dE dU dt if open system itself is at rest and e = u + V2/2 + gz) For a simple compressible fluid, (Sub. dt V2 V2 dU Q W m (ui pi vi i gzi ) m(u e pe ve e gz e ) dt 2 2 or using enthalpy, which is defined as h = u + pv V2 V2 dU Q W m (hi i gz i ) m(he e gz e ) dt 2 2 For an open system, steady flow (all properties at each section remain constant with respect with time) V 2 Vi 2 g z z q w (he hi ) e e i 2 This is the most frequently used form of the first law equation for steady flow systems because many steady flow systems have only one inlet and one outlet, one dimensional flow is a common assumption and effects of electricity, magnetism and surface tension are negligible.
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